1. Locate and label the points and identify their quadrants: - Point (-1, -3) is in Quadrant III (both x and y negative). - Point (4, -2) is in Quadrant IV (x positive, y negative). - Point (-2/5, 4) has x negative and y positive, so it is in Quadrant II. - Point (6, 0) lies on the positive x-axis, so no quadrant. - Point (-4, 5) is in Quadrant II. - Point (3, 0) lies on the positive x-axis. - Point (1, 1) is in Quadrant I. - Point (0, -6) lies on the negative y-axis. 3. For Figure 2.21(a): (a) Estimate values: - $f(0) \approx 1$ - $f(2) \approx 2$ - $f(4) \approx 3$ - $f(-2)$ is outside the domain shown (x from -2 to 4), but graph likely starts at x = -2, so approximate $f(-2) \approx 0$ (b) Domain: $[-2, 4]$ (c) Range: approximately $[0, 3]$ (d) x-intercept: at $x = -2$, where $f(-2) = 0$ 4. For Figure 2.21(b): (a) Estimate values: - $f(0) \approx 0$ - $f(2) \approx 1.5$ (b) Domain: approximately $[0, 4]$ (c) Range: approximately $[0, 2]$ (d) x-intercept: at $x = 0$ 5. For Figure 2.22(a): (a) Estimate values: - $f(0) \approx 0$ - $f(1) \approx 1$ - $f(-1)$ roughly out of domain (x starts at $-1$), at $x=-1$, $f(-1) \approx 0$ (b) Domain: approximately $[-1, 4]$ (c) Range: approximately $[0, 3]$ (d) x-intercept: at $x=0$ and $x=-1$ 6. For Figure 2.22(b): (a) Estimate values: - $f(0)$ undefined (domain from 1 to 4) - $f(2) \approx 2$ - $f(3) \approx 2$ - $f(4) \approx 2$ (b) Domain: $[1,4]$ (c) Range: approximately $[1,3]$ (d) x-intercept: none visible (minimum y about 1) 29. $s = f(t) = \sqrt{t^2 - 9}$ - Domain requires the radicand $t^2 - 9 \geq 0 \Rightarrow |t| \geq 3$ 30. $F(r) = -1/r$ - Domain: $r \neq 0$ 31. $f(x) = |7x - 2|$ - Absolute value function, domain: all real numbers. 32. $v = H(u) = |u - 3|$ - Domain: all real numbers. 33. $F(t) = 16/t^2$ - Domain: $t \neq 0$ 34. $y = f(x) = 2/(x - 4)$ - Domain: $x \neq 4$ 35. Piecewise function: - $g(p) = p + 1$ if $0 \leq p < 7$ - $g(p) = 5$ if $p \geq 7$ 36. Piecewise function: - $g(x) = x$ if $0 \leq x < 1$ - $g(x) = x^2 - 2x + 2$ if $x \geq 1$ 37. Piecewise function: - $g(x) = x + 6$ if $x \geq 3$ - $g(x) = x^2$ if $x < 3$ 38. Piecewise function: - $f(x) = x + 1$ if $0 < x \leq 3$ - $f(x) = 4$ if $3 < x \leq 5$ - $f(x) = x - 1$ if $x > 5$ 39. Functions from Figure 2.23: - (a) No, it’s not a function (fails vertical line test). - (b) Yes, it is a function. - (c) Yes, it is a function. - (d) Yes, it is a function. 40. One-to-one functions from Figure 2.24: - (a) No, has a typical parabola shape, not one-to-one. - (b) No, oscillates and not one-to-one. - (c) No, piecewise with flat section. - (d) Yes, strictly increasing with no horizontal overlaps.